The Simplifier

THE PRECEDENCE RULE
The first rule of mathematics is the rule that guides us on how we respect the operators. This rule tells us which operator to consider first before the other in cases where more than just one of the operators exist together. 

Note that we most often handle mathematical processes from left to right except in few special occasions and we do this by obeying a rule known as precedence rule. More generally we know this rule as BODMAS.

BODMAS is an acronym for:

1. B for Bracket ⇒ (parenthesis), [square bracket], {curly braces}
2. O for Of (*) ⇒ this a statement that tells us to also multiple
3. D for Division (÷)
4. M for Multiplication (*)
5. A for Addition (+)
6. S for Subtraction ( - )

Note also that we could be faced with roots, powers and other operators and such special operators are considered first before these ones stated above, however for now let's deal with the basics.

Keynote
Every mathematical problem follows a sequence called the precedence rule – almost every aspect of life follows a pattern!

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The Simplifier

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Example One 1. Simplify: 1 + 1 – 1 x 1 ÷ (1 + 1) of 1 Step 1: Recall the precedence Rule as: • Starting from left to right and • Following the BODMAS sequence  We start the part with bracket : 1 + 1 – 1 x 1 ÷ (1 + 1) of 1 = 1 + 1 – 1 x 1 ÷ 1 of 1 Next we move to the part with the of : 1 + 1 – 1 x 1 ÷ 1 of 1 = 1 + 1 – 1 x 1 ÷ 1 (Note: 1 of 1 = 1 * 1 = 1) Next we move to where we have a division : 1 + 1 – 1 x 1 ÷ 1 = 1 + 1 – 1 x 1 Next is to handle the Multiplication : 1 + 1 – 1 x 1 = 1 + 1 – 1 (Note the negative sign in front of 1 i.e. – 1 x 1) Next to be considered is Addition and Finally Subtraction : 1 + 1 – 1 = 2 – 1 = 1 Keynote This sequence is maintained even if more than one type of the same operator exists at different locations - finish with all additions  before subtractions. Applicable to all others operators!
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